# LTI system impulse response [closed]

I am learning signal processing and need some help with this question

$$h[n]=-x[n]+2x[n-1]-3x[n-3]$$

Given the following input signal $$x[n]$$ calculate y[n] the output of the system $$x[0]=2, x[1]=0, x[2]=1, x[3]=-1$$

What is my first step?

• First step is to copy the question on your homework correctly into what you have written above. – Dilip Sarwate Apr 15 at 15:17

Firt Step would be to figure out $$h[n]$$ as a finite length sequence.
Like your input $$x[n] = \{ \hat{2}, 0, 1, -1 \}$$.
And, given $$h[n] = -x[n]+2x[n-1]-3x[n-3]$$, put $$x[n]=\delta[n]$$ and get $$h[n]$$ as a finite length sequence.
And, then convolve $$h[n]$$ with $$x[n]$$ to get the output $$y[n]$$.